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Computing rank-revealing factorizations of matrices stored out-of-core
dc.contributor.author | Heavner, Nathan | |
dc.contributor.author | MARTINSSON, GUNNAR | |
dc.contributor.author | Quintana-Ortí, Gregorio | |
dc.date.accessioned | 2023-07-21T09:13:47Z | |
dc.date.available | 2023-07-21T09:13:47Z | |
dc.date.issued | 2023-04-17 | |
dc.identifier.citation | Heavner N, Martinsson PG, Quintana-Ortí G. Computing rank-revealing factorizations of matrices storedout-of-core.ConcurrencyComputatPractExper. 2023;e7726. doi: 10.1002/cpe.7726 | ca_CA |
dc.identifier.uri | http://hdl.handle.net/10234/203470 | |
dc.description.abstract | This paper describes efficient algorithms for computing rank-revealing factorizations of matrices that are too large to fit in main memory (RAM), and must instead be stored on slow external memory devices such as disks (out-of-core or out-of-memory). Traditional algorithms for computing rank-revealing factorizations (such as the column pivoted QR factorization and the singular value decomposition) are very communication intensive as they require many vector-vector and matrix-vector operations, which become prohibitively expensive when data is not in RAM. Randomization allows to reformulate new methods so that large contiguous blocks of the matrix are processed in bulk. The paper describes two distinct methods. The first is a blocked version of column pivoted Householder QR, organized as a “left-looking” method to minimize the number of the expensive write operations. The second method results employs a UTV factorization. It is organized as an algorithm-by-blocks to overlap computations and I/O operations. As it incorporates power iterations, it is much better at revealing the numerical rank. Numerical experiments on several computers demonstrate that the new algorithms are almost as fast when processing data stored on slow memory devices as traditional algorithms are for data stored in RAM. | ca_CA |
dc.format.extent | 22 p. | ca_CA |
dc.format.mimetype | application/pdf | ca_CA |
dc.language.iso | eng | ca_CA |
dc.publisher | Wiley | ca_CA |
dc.rights | © 2023 The Authors. Concurrency and Computation: Practice and Experience published by John Wiley & Sons Ltd. | ca_CA |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | ca_CA |
dc.subject | blocked matrix computations | ca_CA |
dc.subject | householder QR factorization | ca_CA |
dc.subject | HQRRP factorization | ca_CA |
dc.subject | out-of-corecomputation | ca_CA |
dc.subject | partial rank-revealing factorization | ca_CA |
dc.subject | randomized numerical linear algebra | ca_CA |
dc.subject | randUTV factorization | ca_CA |
dc.subject | rank-revealing factorization | ca_CA |
dc.subject | shared-memory multicore processors | ca_CA |
dc.subject | shared-memory multiprocessors | ca_CA |
dc.title | Computing rank-revealing factorizations of matrices stored out-of-core | ca_CA |
dc.type | info:eu-repo/semantics/article | ca_CA |
dc.identifier.doi | https://doi.org/10.1002/cpe.7726 | |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | ca_CA |
dc.type.version | info:eu-repo/semantics/publishedVersion | ca_CA |
project.funder.name | Office of Naval Research | ca_CA |
project.funder.name | National Science Foundation | ca_CA |
project.funder.name | Department of Energy ASCR | ca_CA |
project.funder.name | Nvidia Corp. | ca_CA |
project.funder.name | Ministerio de Ciencia, Innovación y Universidades (Spain) | ca_CA |
project.funder.name | Agencia Estatal de Investigación (AEI), Spain | ca_CA |
project.funder.name | FEDERfunds(MCIN/AEI/FEDER/UE) | ca_CA |
oaire.awardNumber | N00014-18-1-2354 | ca_CA |
oaire.awardNumber | DMS-1952735 | ca_CA |
oaire.awardNumber | DMS-2012606 | ca_CA |
oaire.awardNumber | DE-SC0022251 | ca_CA |
oaire.awardNumber | t PID2021-123627OB-C55 | ca_CA |
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